Computer simulation of the mechanically-assisted failing canine circulation

Detection of growth-restricted fetuses using a patient-specific model

Fetal growth restriction (FGR) is one of the major contributors to adverse perinatal outcome. The purpose of this work was to extend the use of Ultrasound Doppler measurements and allow early and accurate detection of FGR. To this end, a mathematical model was developed to represent the major fetal hemodynamic mechanisms involved. Based on model parameters' values, the forward model predicted flow waveforms at the locations where Doppler measurements are routinely performed. Blood velocity waveforms measured in 20 FGR and 20 normal fetuses were used as inputs to an inverse model solution to obtain the parameters' values of the specific fetus. Model predictions indicated significant changes in the circulation of FGR fetuses compared to normal fetuses. Estimated cardiac output was significantly lower in the FGR group compared to the control group (330 ± 52 ml min(-1) Kg(-1) compared to 396 ± 52 ml min(-1) Kg(-1), P<0.001). Also, estimated cardiac output distribution towards the placenta was lower for the FGR group (145 ± 49 ml min(-1) Kg(-1) compared to 181 ± 31 ml min(-1) Kg(-1), P<0.01). In the FGR group the model indicated also significant increase in estimated cardiac output distribution towards the brain (9.6 ± 0.7%, compared to 8.0 ± 1.6 %, P<0.01) and in the degree of blood shunted by the ductus venosus (60.6 ± 17.7 %, compared to 39.7 ± 14.8 %, P<0.01), indicating severe brain-sparing state in these fetuses. We conclude that patient-specific mathematical modeling is a promising direction for personalizing and optimizing the treatment options in pregnancies complicated by fetal growth-restriction.

Cardiovascular simulation toolbox

A toolbox for Matlab Simulink (trademark of Mathworks corp. etc.) was developed to simulate various models of flow in the cardiovascular system and study effects of different pathological conditions. The toolbox was based on well-known analog lumped models of blood flow in vessels, the varying elastance heart model, blood flow through vessels, shunts, and valves as well as models of oxygen exchange at lungs and tissue. The toolbox is modular providing the basic building blocks of the cardiovascular system. Parameters for the individual components may be set by the user to adapt the component to the simulated system. Several examples are shown. This modeling system is described and is also available for downloading as an open source for free use. The authors see this as the basis for wide collaboration and standardization in modeling. A web site will be available for accepting contributions from other researchers and to create a free exchange.

Estimation of forward and backward mitral flow using indicator dilution technique: a theoretical feasibility study

A new theoretical algorithm is presented for high-resolution mitral flow determination based on the indicator dilution principle. The algorithm allows forward as well as backward time-dependent mitral flow estimation with a beat-to-beat resolution. Indices of normal/subnormal left heart functioning, including total stroke volume (TSV), cardiac output (CO), total ejection fraction (TEF), mitral regurgitation volume (MRV) and mitral regurgitation fraction (MRF), are determined. Knowledge of left atrium and ventricle indicator concentration versus time dependencies and the end systolic left atrium and ventricle volumes are sufficient to determine the mitral flow pattern. However, the non-dimensional index of the total ejection fraction can be calculated on the basis of only the indicator concentration. The algorithm was validated by applying it to blood flows and heart chamber volumes derived from a computer simulation of the cardiovascular circulation. First left heart concentrations versus time data were obtained by determining the distribution over a cardiovascular tract of an ideal indicator, a bolus of which was intravenously injected into one of the arms. Then the backward problem of finding mitral flow was solved. The accuracy of the mitral flow estimation depends on the accuracy of end systolic left atrium and ventricle volume data. The method is applicable over a wide range of aortic regurgitation, up to 20% of cardiac output, suggesting that the algorithm might become a robust technique of non-invasive mitral flow assessment, replacing traditional techniques such as nuclear radiography.

Intraoperative monitoring of IMA flow: what does it mean?

BACKGROUND

This study examines whether the measurement of internal thoracic artery (ITA) graft flow can determine the adequacy of the ITA-left anterior descending coronary artery (LAD) anastomosis.

METHODS

To study a wide range of clinical problems, we used a computer simulation of the cardiovascular system. The model included a time-varying elastance model of the heart, a systemic circulation represented by a multielement nonlinear model of the aorta and its major branches, a nonlinear model of the LAD circulation, and a model of the ITA bypass graft.

RESULTS

With a mild LAD stenosis, ITA graft flow was low and flow reversal occurred. As the percent stenosis increased, ITA flow and the percentage of ITA-to-total LAD flow increased. The ITA graft helped to maintain resting LAD blood flow. A partial obstruction (40%) at the ITA-LAD anastomosis reduced ITA graft flow at similar levels of LAD stenosis. However, overlap in flow values comparing a normal with a partially obstructed anastomosis occurred.

CONCLUSIONS

Flow patterns in the ITA are highly dependent on the degree of stenosis of the LAD as well as the integrity of the anastomosis. The predictive power of ITA flow measurement increases with severe stenosis or total occlusion of the proximal LAD and with high coronary blood flow demands.

Computer simulation of cerebrovascular circulation: assessment of intracranial hemodynamics during induction of anesthesia

OBJECTIVE

The purpose of this project was to develop a computer model of cerebrovascular hemodynamics interacting with a pharmacokinetic drug model to examine the effects of various stimuli on cerebral blood flow and intracranial pressure during anesthesia.

METHODS

The mathematical model of intracranial hemodynamics is a seven-compartment, constant-volume system. A series of resistance relate blood and cerebrospinal fluid fluxes to pressure gradients between compartments. Arterial, venous, and tissue compliance are also included. Autoregulation is modeled by transmural pressure-dependent, arterial-arteriolar resistance. The effect of a drug (thiopental) on cerebrovascular circulation was simulated by a variable arteriolar-capillary resistance. Thiopental concentration was predicted by a three-compartment, pharmacokinetic model. The effect site compartment was included to account for a disequilibrium between drug plasma and biophase concentrations. The model was validated by comparing simulation results with available experimental observations. The simulation program is written in VisSim dynamic simulation language for an IBM-compatible PC.

RESULTS

The model developed was used to calculate the cerebral blood flow and intracranial pressure changes that occur during the induction phase of general anesthesia. Responses to laryngoscopy and intubation were predicted for simulated patients with elevated intracranial pressure and non-autoregulated cerebral circulation. Simulation shows that the induction dose of thiopental reduces intracranial pressure up to 15%. The duration of this effect is limited to less than 3 minutes by rapid redistribution of thiopental and cerebral autoregulation. Subsequent laryngoscopy causes acute intracranial hypertension, exceeding the initial intracranial pressure. Further simulation predicts that this untoward effect can be minimized by an additional dose of thiopental administered immediately prior to intubation.

CONCLUSION

The presented simulation allows comparison of various drug administration schedules to control intracranial pressure and preserve cerebral blood flow during induction of anesthesia. The model developed can be extended to analyze more complex intraoperative events by adding new submodels.

Numerical simulation of the blood flow in the human cardiovascular system

This paper describes a numerical model of the human cardiovascular system. The model is composed of 15 elements connected in series representing the main parts of the system. Each element is composed of a rigid connecting tube and an elastic reservoir. The blood flow is described by a one-dimensional time-dependent Bernoulli equation. The action of the ventricles is simulated with a Hill's three-element model, adapted for the left and right heart. The closing of the four heart valves is simulated with the aid of time-dependent drag coefficients. Closing is achieved by letting the drag coefficient approach infinity. The resulting system of 32 non-linear ordinary differential equations is solved numerically with the Runge-Kutta method. The results of the simulation (pressure-time and volume-time dependence for the atria and ventricles and pressure forms in the aorta at a heart rate of 70 beats per minute) agree with the physiological data given in the literature. The model's input aortic impedance is 31.5 dyn s cm-5 which agrees with literature data given for aortic input impedance in man 26-80 dyn s cm-5). Long-term stability of the system was achieved. The cardiovascular system presented here can also be simulated at higher and varying heart rates--up to 200 beats per minute. The results of calculations for some pathological changes (e.g. valvular abnormalities) are discussed.

A study of optimal configuration and control of a multi-chamber balloon for intraaortic balloon pumping

Balloon configuration and control scheme are important for the optimization of assistance of the failing heart with an intraaortic balloon pumping device. In this work, the configuration of a multi-chamber balloon and control schemes have been investigated by using a hemodynamic model and computer simulation methods. Following the simulation study, physical testing and animal experiments were performed to demonstrate the simulation results. Results show that the optimal configuration and controlled multi-chamber balloon can provide better assistance to the failing heart. Based on the simulation and experimental results, it was found that the shape of the rear chamber of a multi-chamber balloon is critical. The optimal control scheme was to inflate the rear chamber first and deflate it last.

Mathematical model of cardiovascular mechanics for diagnostic analysis and treatment of heart failure: Part 1. Model description and theoretical analysis

The planning of drug therapy for heart failure should involve both the diagnostic analysis of the patient's defective state and a prediction of the drug effects on the identified state. We have devised a mathematical model of cardiovascular system mechanics, on which both quantitative diagnosis and evaluation of drug effects can be made. The model was composed of systemic and pulmonary circulatory networks including the dynamics of the left and right ventricles. The model of the ventricles can represent both systolic and diastolic problems in heart failure through the parameters of ventricular contractility and diastolic stiffness. Each vascular network was composed of arterial and venous resistances and total vascular capacitance. Patient's ventricular and vascular parameters were estimated simultaneously from the clinically measurable haemodynamic variables based on the model. Despite the simplicity of the model, the results showed good agreement with clinical and experimental data. The clinically significant haemodynamic classification of heart failure by Forrester et al. (Forrester et al., 1977) was simulated well by the model. This model provides a useful basis for analysing pathophysiological states in heart failure and evaluating drug effects on the disease.

A computer model for analysis of fluid resuscitation

Injuries involving massive blood loss, such as burns, combat wounds, and injuries resulting from car accidents, require fluid resuscitation. The risk involved in fluid therapy is overloading of the circulation, resulting in pulmonary edema which can lead to death. The risk of pulmonary edema may be eliminated by proper determination of maximal infusion volume and rate. Reabsorption of fluid from the extravascular compartment and infusion of fluid following blood loss results in reduction of the hematocrit. This is accompanied by an increase in the heart's preload and afterload. Coronary driving pressure and flow increase due to increased volume. However, because of the reduced hematocrit this increase in coronary flow may not be sufficient to compensate the myocardium, in terms of oxygen supply, for the increase in oxygen consumption. A model of the cardiovascular system, including an extravascular compartment, was designed to analyze the effects of fluid infusion on hemodynamic variables, cardiac oxygen balance, and the redistribution of fluid between intravascular and extravascular compartments. The results indicate that edema is not the only possible adverse effect of overloading the cardiovascular system with fluid. The simulation demonstrated that in certain cases the heart's oxygen balance can become negative. Limiting the rate of infusion can reduce this risk.

A blood vessel model based on velocity profiles

A simple model of pressure-flow relationship in blood vessels was developed. The calculation of the model components was based on velocity profiles in the vessels. The flat velocity profile in the entrance of the vessel was considered. By using mean pressure over the cross-section and assuming a polynomial approximation of the velocity profile, it is shown that the resistance of a vessel segment increases with increased flatness of the velocity profile. Moreover, the analysis provides a means to calculate the resistance of a vessel segment based on the shape of the velocity profiles in that segment. The analysis shows that the inertance element of the segment is not affected by the shape of the velocity profile.

Coronary autoregulation and optimal myocardial oxygen utilization

The complex relationship among myocardial contractility, preload, afterload, and coronary autoregulation was studied using both analytical and numerical methods. To study autoregulation and coronary reserve changes in response to changes in cardiac oxygen consumption and in arterial pressure generation, a new variable was introduced: myocardial resistance to oxygen flow (RO2). This variable was defined as the ratio of the coronary driving pressure to left-ventricular oxygen uptake. High values for this variable indicate small consumption relative to the generated aortic pressure. Conditions which produce the highest obtainable value for RO2 are considered as optimal. An expression relating RO2 to ventricular hemodynamic variables was developed and studied using a mathematical model of the cardiovascular system. The model included a mechanism of local autoregulation based on the assumption that, in steady state, the amount of oxygen consumed equals the amount extracted from coronary blood. Heart rate, peripheral resistance, end-diastolic volume, and myocardial contractility were varied while the coronary circulation was adjusted to meet ventricular oxygen consumption at each state. The model predicts that, for each state of the circulation, there is an optimal level of cardiac contractility for which the coronary reserve is maximized.